In this paper we consider a generalized version of the classical preemptive open shop problem with sum of weighted job completion times objective. The main result is a (2 + ε)-approximation algorithm for this problem. In the last section we also discuss the possibility of improving our algorithm.

Many problems in industry are a form of open-shop scheduling problem (OSSP). We describe a hybrid approach to this problem which combines a Genetic Algorithm (GA) with simple heuristic schedule building rules. Excellent performance is found on some benchmark OSS problems, including improvements on previous best-known results. We describe how our approach can be simply amended to deal with the m...

We present a comprehensive complexity analysis of classical shop scheduling problems subject to various combinations of constraints imposed on the processing times of operations, the maximum number of operations per job, the upper bound on schedule length, and the problem type (taking values “open shop”, “job shop”, “mixed shop”). It is shown that in the infinite class of such problems there ex...

Preemptive open shop scheduling can be viewed as an edge coloring problem in a bipartite multigraph. In some applications, restrictions of colors (in particular preassignments) are made for some edges. We give characterizations of graphs where some special preassignments can be embedded in a minimum coloring (number of colors = maximum degree). The case of restricted colorings of trees is shown...

In this paper, we propose 260 scheduling problems whose size is greater than that of the rare examples published. Such sizes correspond to real dimensions of industrial problems. The types of problems that we propose are : the permutation flow shop, the job shop and the open shop scheduling problems. We restrict us to basic problems : the processing times are fixed, there are neither set-up tim...

The paper considers a three-machine shop scheduling problem to minimize the makespan, in which the route of a job should be feasible with respect to a machine precedence digraph with three nodes and one arc. For this NP-hard problem that is related to the classical flow shop and open shop models, we present a simple 1.5approximation algorithm and an improved 1.4-approximation algorithm.